Analyzing Distribution Transformer Degradation
with Increased Power Electronic Loads
Bhaskar Mitra, Ankit Singhal, Soumya Kundu and James P. Ogle
arXiv:2210.14824v1 [eess.SY] 26 Oct 2022
Electricity Infrastructure and Buildings Division
Pacific Northwest National Laboratory
Richland, WA 99354, USA
Email: {bhaskar.mitra, ankit.singhal, soumya.kundu, james.ogle}@pnnl.gov
Abstract—The influx of non-linear power electronic loads into
the distribution network has the potential to disrupt the existing
distribution transformer operations. They were not designed
to mediate the excessive heating losses generated from the
harmonics. To have a good understanding of current standing
challenges, a knowledge of the generation and load mix as well
as the current harmonic estimations are essential for designing
transformers and evaluating their performance. In this paper,
we investigate a mixture of essential power electronic loads for
a household designed in PSCAD/EMTdc and their potential
impacts on transformer eddy current losses and derating using
harmonic analysis. The various scenarios have been studied with
increasing PV penetrations. The peak load conditions are chosen
for each scenario to perform a transformer derating analysis.
Our findings reveal that in the presence of high power electronic
loads (especially third harmonics), along with increasing PV
generation may worsen transformer degradation. However, with
a low amount of power electronic loads, additional PV generation
helps to reduce the harmonic content in the current and improve
transformer performance.
Index Terms—eddy current, harmonics, power transformer,
PV, THD
I. I NTRODUCTION
Power electronic loads have found a wider application in
power system networks especially after their advancement in
the late 1900s. Many loads require essential power electronic
converters for stage conversion. Some common examples of
power electronic loads include uninterrupted power supply
(UPS) devices, personal computers, laptops, electric vehicle
chargers, etc. These non-linear loads contribute to non-linear
sinusoidal currents. The non-sinusoidal currents, when passing
through network impedance, create a non-sinusoidal voltage
drop [1]. The non-sinusoidal voltage and current components
are integer multiples of the fundamental component called
“harmonics”. The deterioration of the supply voltage creates
stress on the electrical equipment and can potentially damage
it, resulting in increased operating costs and downtime [2].
Increased voltage and current harmonics are found to have
a direct relationship to premature aging and degradation of
transformers. Initial transformer designs were made considering conventional load models, i.e., Constant Impedance
(Z), Constant Current (I), and Constant Power (P) or “ZIP”
This work was supported by the Sensors and Data Analytics Program of
the U.S. Department of Energy Office of Electricity, under Contract No. DEAC05-76RL01830.
models, that would operate at fundamental 60Hz or 50Hz
frequency [3, 4]. Under the increased penetration of non-linear
loads, the design of power transformers needs to be reassessed
to ensure proper and safe operation. Increased non-linear loads
increase the transformer losses due to overheating of the core,
creating a larger derating factor [5, 6].
The problem of harmonics is more evident with customers
on the low-voltage end. The common household equipment
includes but not limited to desktops, laptops, LED lamps,
variable speed drives, solar panels, etc. To compound the
challenges, as more and more electric vehicles come to the
market, they rely majorly on at-home charging that produces
a large fraction of non-linear voltage and current. Certain
power electronic devices like VFD’s contribute more 3rd
harmonics, if they are not properly compensated it would lead
to additional losses and loss-of-life for the transformer. The
addition of harmonics has an effect on transformer protection
as well. Addition of the 5th harmonic needs to be compensated
below a certain threshold before the protection relays can be
engaged. The distorted harmonic waveforms results in loss of
essential information for protection, this might result in the
protection devices operating slower [7].
Currently, there is a gap in high-fidelity load models that can
capture the typical characteristics of non-linear models, i.e.,
the cross-coupling effect of voltages and current. A harmonicrich current/voltage dataset is essential to understand the effect
on transformer losses, heating, etc. “ZIP” based harmonic load
models suffer from a lack of enhanced harmonic spectrum that
can be observed through the operation of various non-linear
devices [8]. Real-world field data is not publicly available to
perform such analysis. Methods relying on laboratory setups
to develop such datasets fail to capture the effect on other
nonlinear load currents.
Therefore, in this paper, (i) we perform an analysis of
residential transformer heating and losses encountered due to
the presence of non-linear power electronic residential loads
using PSCAD/EMTdc. Detailed power electronic models are
developed to create harmonic rich datasets to entail their effect
on transformer operation; (ii) Different loading scenarios on
the transformer are assessed with increasing PV penetration
to understand its effect on THD(%), eddy current losses, and
the subsequent impact on transformer derating.
The rest of the paper has been organized in the following
sequence. FFT performs the computation of the DFT matrix
as a product of sparse factors. The DFT for such a sequence
can be given as (1),
X[k] =
N
−1
X
x[n]e−j2πkn/N
(1)
n=0
Fig. 1: Schematic representation of the simulation setup in PSCAD.
way. Section II discusses the modeling approach for the study.
Section III discusses the calculation of eddy current losses
due to nonlinear harmonic current in transformers. Section IV
discusses the results, and Section V concludes the paper with
major findings and proposed future enhancements.
II. M ODELING
A. System Description
Usually, the residential customers are supplied through a
single split-phase connection in the USA. In this work, we
are modeling 5 houses that have been connected to a 7.2 kV
distribution transformer, as shown in Fig. 1. Each home is
comprised of four power electronic load combinations shown
in Table I and discussed in detail in [9].
TABLE I. Power electronics-based load models representing house appliances
Load model
Rectifier + Buck DC-DC converter
Rectifier + Flyback DC–DC converter
VFD + Induction motor
Boost converter + inverter
House appliances
Desktop, home entertainment
Laptop charger
HVAC, washer, dryer
PV system, EV charger
B. Data Generation
The power electronic load combinations were modeled
using PSCAD/EMTdc. The steady-state values of current were
recorded at the secondary of the distribution transformer as
shown in Fig. 1. A similar process was repeated for several
load combinations, and a few scenarios were selected that
draw significantly harmonic-rich current for further analysis
as discussed in Section IV.
III. T RANSFORMER D EGRADATION A NALYSIS DUE TO
H ARMONICS
Most power electronic loads are fitted with a single or
distributed capacitor at the terminal that helps to maintain a
constant dc voltage along with the parasitic inductors. Since
there is a periodic change in the load impedance, the current
waveform varies from the supplied voltage waveform. The
non-sinusoidal current can be represented as a sum of the
fundamental and integer multiple of the fundamental “harmonics”.
A. Fast Fourier Transform (FFT)
One can transform a given sequence in time into its respective frequency components using Discrete Fourier Transform
(DFT) [10]. FFT is useful for performing the DFT of a
where N is the length of the signal. Since the sampling
frequency of the signal is 20kHz, the maximum represented
frequencies are half of the sampling frequency. We try to
capture all the representative frequencies in that range. The
harmonic components in the measured current are a function
of the fundamental 60Hz frequency. A frequency scan is
performed to identify the magnitude of the current harmonics
Ih .
Since the measured signal is not an integer multiple, the
endpoints of the frequency spectrum are discontinuous. FFT
produces a smeared spectral version of the original signal
where the energy of one frequency leaks into adjacent frequencies. This phenomenon is known as spectral leakage. To get
the best estimate of the current harmonics, we perform a scan
of the frequencies adjacent to the integer harmonic frequency.
Practices like windowing are utilized to reduce the effect of
the non-integer frequencies, but this was not considered as a
part of our work.
B. Eddy Current Losses
In a residential set-up, most of the losses are due to heating
I 2 R losses. A residential home consists of both linear and
non-linear loads; in this study, we majorly focus on the
increase in non-linear residential loads that create harmonics
that inadvertently contribute to more losses. The effect is more
tremendous at the grid-edge locations where a lot of power
electronic loads are connected, for example, the distribution
service transformers.
The losses occurring in a transformer can be divided into
two categories (2), (i) No-Load losses and (ii) Load losses. In
this paper, we study the losses due to non-linear loads. When
current flows through a conductor, it generates heat which is
either utilized or lost in the surrounding environment.
T rLoss = T rN L + T rLL
(2)
The load losses (T rLL ) can be further subdivided into a
summation of eddy current losses (T rEC ) and structural stray
losses (T rST ).
The eddy current component can be written as (3),
T rEC =
hX
max
Ih2 Rh
(3)
h=1
The winding losses increase as a square of the harmonic current component (Ih ), Rh is the effective resistance comprising
of the non-frequency dc component and the resistance that
varies with harmonic content. When harmonic current flows
through the conductive materials of the transformer, it leads
to a variation in temperature.
TABLE II. Scenarios of different load combinations with increasing PV
penetration
From Newton’s law of cooling (4),
P δt = mcδθ + αθAδt
(4)
where P is the I 2 R losses for material, m is the mass of the
material, c is the specific heat capacity of the material, δθ rise
of temperature above ambient temperature for time δt, A is
the surface area of the material and α is the emissivity factor.
The change in temperature can be written as (5) [11],
θ(t) = θf inal [1 − e−t/τ ]
Scenarios
PV units
1
2
3
4
5
0
1
2
3
4
Peak Load
Time
evening
evening
evening
day
day
Total PV
generation
0 kW
1.5 kW
3 kW
10.5 kW
14 kW
Total other
load
9.5 kW
9.5 kW
9.5 kW
2.5 kW
2.5 kW
Net load
9.5 kW
8 kW
6.5 kW
-8 kW
-11.5 kW
(5)
In steady state (4), mcδθ = 0 and (4) can be re-written as
(6),
P δt = αθAδt,
P
θ = αA
(6)
From (6), we can say that θ ∝ P ∝ I 2 Rh , as more nonlinear current passes through the transformer, the ambient
temperature of the material changes, resulting in more losses.
Rh = RDC + h2 PEC−R
(7)
th
where RDC is the dc-winding resistance at h harmonic and
PEC−R is the winding eddy current loss factor, that ranges
between 0.01 in low voltage transformers to 0.10 for substation
transformers. For our study, we consider PEC−R as 0.05.
By replacing Rh in (3), we get
T rEC = I12 RDC +
hX
max
Ih2 h2 PEC−R
(8)
h=3,5,7,...
The first term of (8) I12 RDC is the non-frequency dependant
part, and Ih2 h2 PEC−R reflects the frequency dependant part of
the transformer eddy current losses. Thus, the harmonic driven
transformer eddy current losses can be summarized as (9),
T rEC = PEC−R
hX
max
I 2 h2
(9)
h=1
C. Harmonic Loss Factor & Transformer Derating
Harmonic loss factor (FHL ) is defined as the ratio of the
total loss due to eddy current due to harmonics and the winding
current losses in the absence of harmonics [12]. It is expressed
as (10),
Phmax
2 2
h=1 Ih h
FHL = P
hmax 2
h=1 Ih
(10)
To reduce the loss-of-life of a transformer due to an
increased non-linear current, they are usually derated (i.e.,
reduced transformer loading). The derating % helps to understand the transformer operational capability below its rating to
prolong its duration.
Fig. 2: Load combination for 5 houses corresponding to a different scenario,
each scenario represents the peak load condition with a given PV penetration.
IV. R ESULTS AND D ISCUSSION
A. Simulation Setup
To understand the effect of different loading scenarios on
transformers, the simulation setup described in Fig. 1 is used.
A total of 5 scenarios are constructed with different power
electronic load combinations to analyze the impact on the
transformer, as shown in Table II. All these 5 scenarios are
assumed to represent the peak loading condition for a given
transformer with increasing solar PV units. Scenarios 1, 2, and
3 are evening peaking cases where solar generation. Whereas
scenarios 4 and 5 have solar generation high enough to cause
a reverse power peak during daytime when the load is low.
It is assumed that 1 PV unit generates 3.5 kW and 1.5
kW during the daytime and evening, respectively. The exact
loading condition (mix of VFD, laptop, desktop, and PV) of
each of the 5 houses connected to a service transformer in
each scenario is shown in Fig. 2.
B. Impact of increasing PV on Transformer Current Harmonics and Eddy Losses
The current waveforms drawn by the transformer secondary
in all 5 scenarios are shown in Fig. 3. The reverse current
can be noticed in scenarios 3 and 4 due to high solar PV
generation. These waveforms were analyzed to understand the
harmonic contribution in each scenario. The harmonic contents
of the measured current signals were extracted using FFT
Fig. 3: Equivalent transformer secondary current for different scenarios.
as described in Section III-A. The THD(%) for each of the
scenarios was calculated using (11),
qP
hmax 2
h=2 Ih
T HD =
(11)
I1
Where Ih denotes the hth harmonic current magnitude. Eddy
current losses calculations are based on the discussion in
Section III-B. THD(%) and corresponding eddy losses for each
scenario are shown in Fig. 4. It is observed in scenarios 1,
2, and 3 that increasing solar PV units cause more harmonic
distortion in transformer currents. On the contrary, in scenarios
4 and 5, it is observed that the addition of PV generation
decreases THD. To understand this pattern, we need to look
at the frequency spread of 1st , 3rd , and 5th harmonic of the
current as shown in Fig. 5. Observing scenarios 1, 2, and
3, we find that the increasing PV generation reduces the net
fundamental current magnitude as expected. However, the 3rd
harmonic current magnitude remains the same in scenarios
1, 2, and 3, as shown in Fig. 5. It can be inferred that the
PV inverter is primarily compensating for the fundamental
component of the load currents, not the 3rd harmonic. This
leads to an increased % of 3rd harmonic in scenario 3, as
shown in Fig. 6, resulting in high THD(%).
On the other hand, scenarios 4 and 5 have very high PV
generation but a much lower amount of other power electronics
load compared to scenarios 1-3. Therefore, the net current is
mainly composed of PV current. Since PV units are mandated
to maintain less than 5% THD, they come equipped with
harmonic filters by the vendors, as discussed in [9]. Therefore,
in scenarios 4 and 5, harmonic distortions are the lowest.
Transformer eddy losses tend to follow the current THD %
and are shown in Fig. 4. It can be seen that scenario 3 has the
highest eddy losses, close to 30%.
Fig. 4: Variation of THD(%) along with eddy current losses for different load
combinations and PV penetration.
Fig. 5: The harmonic frequency spectrum of the secondary transformer under
various load combinations and PV penetrations.
C. Impact on Transformer Derating
All 5 scenarios represent the peak loading situation for
the given PV penetration. It is important for the transformer
derating analysis as it is usually performed in a full-loading
condition. Note that the up to 2 PV unit penetration (scenario
1-3) peak loading is assumed to occur during the evening
when other loads are high. Whereas, for higher penetration
(scenarios 4-5), solar PV generation can create its own reverse
power peak during the daytime.
Fig. 6: Variation of normalized frequency spectrum of 3rd & 5th harmonic
with respect to fundamental current magnitude with different load and PV
penetration scenarios.
TABLE III. The overall impact of increasing PV penetration on transformer
degradation in terms of THD, eddy current losses, and transformer derating
Scenarios
1
2
3
4
5
THD (%)
18.30
26.51
29.05
5.55
3.52
T rEC (%)
6.89
8.66
9.41
5.22
5.11
Derating (%)
85.59
78.59
75.88
98.01
98.95
The harmonic loss factor helps us to understand the % at
which the transformers should be operated to prolong its life.
The derating % for the different scenarios is shown in the
last column of the Table II. The worst derating is observed
in scenario 3, where the transformer operates at 75.88% of
its rated capacity resulting in significant loss of life. If the
penetration of power electronic loads are further increased
the transformers would need to be further derated for their
operation.
Total impact on the transformer in terms of THD(%), eddy
losses, and derating are listed in Table III. Overall, if PV units
come equipped with a filter as mandated by the standards,
their individual effect on the transformer loading is positive.
Therefore, in the presence of low power-electronic loads
(scenarios 4 & 5), increasing PV penetration has a positive
impact on transformer degradation. However, in the presence
of high power-electronic loads (scenarios 1-3), increasing PV
penetration may have adverse impacts on transformer degradation since it is not able to compensate for the 3rd harmonic
consumed by the loads such as VFDs, thus increasing 3rd
harmonic contribution.
V. C ONCLUSION
The proposed work represents the challenges faced by a
low-voltage distribution transformer due to the high penetration of a power electronic-dominated residential infrastructure
via EMTP simulations. By operating principle, transformers
are linear devices, and the addition of non-linear power electronic loads makes their operation non-linear. The harmonic
load currents increase the losses in a transformer. The nonlinear current causes a rise in temperature that affects the
effective resistance of the transformer, as discussed in the
Section III. The eddy current losses depend on the magnitude
of the harmonic current, and higher THD(%) contributes to
more eddy current losses. Integration of PV resources to
compensate for the transformer loading had an adverse effect
with increased levels of 3rd harmonic. Such scenario’s are
particularly visible for scenario 2 & 3 where the load of the
network is mostly compensated by PV generation. Although,
under low power electronic loading conditions, the addition of
PV helped to reduce THD(%) in the transformer.
To have a better estimate of the transformer performance,
detailed power electronic models are necessary. However, the
scalability of inverter models in different simulation tools
beyond a certain number is infeasible. Thus developing mathematical models of harmonic loads via frequency coupled
matrix (FCM) will be considered in future work to generate
high-fidelity time-series data for further analysis.
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